I. Field of the Invention
This invention relates to the broad field of speed control for brushless DC motors, with respect to which there are a number of prior art methods and apparatus. The present invention is distinguished from the prior art arrangements of which we are aware by providing a unique control arrangement that is relatively simple to implement and yields excellent performance with improved efficiencies of operation.
FIG. 2 shows the idealized back-EMF (BEMF) waveforms of a 30 brushless motor. There is a direct relationship between the BEMF and the torque constant K.sub.t of a brushless motor, where the torque constant is proportional to the BEMF or VEMF constant K.sub.t (.alpha.). The motor's BEMF is the BEMF constant multiplied by the motor's speed: EQU V.sub.EMF =V.sub.EMF (.alpha.)=K.sub.t (.alpha.).omega.=K.sub.t (.alpha.)-K.sub.t .omega. (1)
Thus, the motor's phase torque T.sub.ph (.alpha.) is the product of the torque constant K.sub.t (.alpha.) multiplied by the motor's phase current l.sub.ph : EQU T.sub.ph (.alpha.)=K.sub.t (.alpha.)l.sub.ph (2)
The losses in the motor are partially determined by the phase current. The I.sup.2 R losses PL.sub.cu, or copper losses, in the motor are given by: ##EQU1##
The object of the invention is to control the torque output of the motor and thus its speed while optimizing its efficiency, which is mainly achieved through minimizing its I.sup.2 R losses.
For the purposes of this discussion and without restricting the principle, we will assume that the BEMF waveform is sinusoidal as shown in FIG. 2 and which is a good approximation for the actual BEMF waveform of many brushless motors.
For a given constant current the available torque per phase is: EQU T.sub.ph =f(.alpha.)=T.sub.ph (.alpha.)=K.sub.t .multidot.sin (x).multidot.I.sub.ph (4)
and the output power is: ##EQU2##
The I.sup.2 R losses are: EQU PL.sub.cu =I.sup.2 .multidot.R=i(P).sup.2 R (6)
for a total efficiency of: ##EQU3##
The conventional brushless motor control will maintain a fixed commutation angle of 120.degree. of 180.degree., or 180.degree. of 180.degree.. To reduce the torque output of the motor it is simply required to reduce the total motor current.
This may not be the most efficient operation of the motor, however. Yet this control can be implemented easily by using hall sensors for commutation or one of many sensorless commutation methods to yield an efficient, low cost controller.
A similar reduction in motor torque can be achieved if, instead of lowering the motor current, the current will be conducted for a shorter period of time, preferably at those positions, where the torque constant is the highest.
We can now maximize the expression in (7) and determine the optimal turn-on time for a given power or torque output. From the output torque: ##EQU4## we can determine the current required for a certain torque output: ##EQU5## and the resulting I.sup.2 R losses: ##EQU6## From (9) and (10) we determine the motor efficiency as: ##EQU7## Finally, we can optimize (11) by minimizing (10) which yields: ##EQU8##
Thus, from (12) we determine, for the above assumptions, the motor will operate at its peak efficiency at a commutation angle of 67.degree. centered around the peak torque point; however the conventional method of 6-step commutation results in reduced motor efficiency.
The above analysis had assumed that the current can be fixed regardless of the commutation position of the motor. In most instances, this is not the case but the motor current will depend on the commutation as well there will be a rise time associated with the current. Thus, for a small commutation angle the torque, which can be achieved will be smaller than the above theoretical value and the commutation angles will not be the optimal angles derived above.
Conversely, we can use this feature to control torque, while at the same time commutating the motor with improved efficiency. This can be achieved by designing a commutator with variable commutation angles. The duration of the commutation determines the efficiency of the system, while the commutation position determines the torque. The block diagram of this commutator is shown in FIG. 3. The commutator can be implemented both analog and digitally, as well as using dedicated hardware or a microcontroller.